Developing a multiobjective sustainable supply chain network locationallocation model for perishable products
Shadi Munshi ^{1}, Abdul Aziz AlAnazi ^{1}, M. S. AlAshhab^{ 1, 2}
^{1}^{ }Department of Mechanical Engineering, College of Engineering and Islamic Architecture, Umm AlQura University, Makkah 24211, Saudi Arabia
^{2}^{ }Design and
Production Engineering Department Faculty of Engineering, AinShams University,
Cairo 11511, Egypt

ABSTRACT 

In this paper,
the problem of considering how to design and plan the (SSCN) for perishable
goods has been addressed. The proposed model targeted considerable assistance
from organizations for the efficient design of SCM networks. The model aims
to maximize profit and OCSLs while minimizing the total cost. The proposed
model is formulated using MINLP and solved by GAMS/DICOPT solver. The effects
of the maximum permissible deviation on the different objectives and supply
chain performance are studied. The maximum allowable deviations range from 0
to 0.5 with a step of 0.1. In addition, the effect of changing the
optimization order on the performance of the network performance is studied. 

Received 12 April 2022 Accepted 16 May 2022 Published 31 May 2022 Corresponding Author Shadi Munshi,
DOI 10.29121/granthaalayah.v10.i5.2022.4595 Funding: This research
received no specific grant from any funding agency in the public, commercial,
or notforprofit sectors. Copyright: © 2022 The
Author(s). This work is licensed under a Creative Commons
Attribution 4.0 International License. With the
license CCBY, authors retain the copyright, allowing anyone to download,
reuse, reprint, modify, distribute, and/or copy their contribution. The work
must be properly attributed to its author. 

Keywords: Supply chain, Perishable, Multiobjective,
MINLP, GAMS, FIFO 
1. INTRODUCTION
Some researchers defined Supply chain management (SCM) as the automatic integration of stakeholders starting with demand from customers and passing by needs from suppliers according to the estimation of the enterprise resource planning system AlAshhab et al. (2021). The term "supply management" may be considered for the management of systems to optimize costs of materials, quality, and service Dai et al. (2018). To achieve this optimization, the following operations should be integrated: procurement, transportation, storage, required quality assurance to manage the inventory of materials, as well as the internal distribution of resources. Material Management in the organization includes all aforementioned activities Isaloo and Paydar (2020)
During manufacturing planning activities, the design of SCN plays a vital role in any firm. So, the decision of SCN design is one of the most important taken one in SCN. the design is considered strategic planning of the supply chain Rashidi et al. (2016) It plays a major role in SCM.
Exact methods have been used to solve SSCN design including heuristics plus metaheuristics, LP, NLP, and MILP. Moreover, MINLP models have been also developed (MINLP) AlAshhab and Aldosari (2022). GAMS platform could be used for implementing this mathematical formulation AlAshhab and Aldosari (2022), GAMS (n.d.). Metaheuristic algorithms are also used based on Pareto solutions Rashidi et al. (2016), Zahiri et al. (2017), as in the Genetic Algorithm (GA) Dai et al. (2018), Rashidi et al. (2016), Rohmer et al. (2019), Validi et al. (2014) Gas, as a populationbased technique works effectively for multiobjective optimization problems. Konak et al. (2006) Holland et al developed the concept of GA in the early 1960s and 1970s (Rate & a Cue, n.d.).
Schaffer (1985) has proposed the first multiobjective GA, called vector evaluated GA (or VEGA). Niched Pareto Genetic Algorithm (NPGA), Subsequently, Horn et al. (1994) developed several multiobjective evolutionary algorithms, including the multiobjective Genetic Algorithm (MOGA) Kocabay and Alaçam (2017) the Weight Based Genetic Algorithm (WBGA) Hajela and Lin (1992) Random Weighted Genetic Algorithm (RWGA) Konak et al. (2006) Nondominated Sorting Genetic Algorithm (NSGA) (Konak et al., 2006). Particle Swarm Optimization (PSO) Patidar et al. (2018), and Simulated Annealing (SA) Chalmardi et al. (2019), EskandariKhanghahi et al. (2018)
εconstraint technique, is also used by researchers Arvan et al. (2015), Rohmer et al. (2019) Some of them devised a solution strategy to solve their model, based on Lagrangian relaxation and εconstraint Diabat et al. (2019) Some models Isaloo and Paydar (2020), Yakavenka et al. (2020) Production and distribution planning are the two main optimization problems in the supply chain and their decisions are often made separately. The process begins with production and then continues to product distribution from manufacturers to consumers. However, competition resulting from globalization, and various competitors in the local market requires that the supply chain in the company guarantee its resource efficiency, increase its service level for consumers, and reduce lead time and stock Herlina (2022)
The profit and overall service level of the customers are greatly affected by production planning effects. Therefore, it is very important to pay more attention to the production planning process to ensure a highprofit level and high service level on the other side AlAshhab (2016) Other aspects such as environmental or economic impact, have urged academic researchers to consider them due to their importance. Some of them created biobjective models that took into account both economic and environmental objectives, in which environmental consequences, are designed to reduce CO2 emissions AlAshhab et al. (2021) as in designed proposed models. The main or first objective Trisna et al. (2016) is to minimize total cost in the framework of multiobjective function in the supply chain.
This study discusses the design and plan of an SSCN for perishable products to maximize SC profit, and the OCSLs, and minimize total cost. A mathematical model has been devised to design a multiperiod model that is sustainable for three suppliers, a manufacturer, a retailer, and one warehouse. The problem is reformulated using MINLP.
The model's aim is to find out the best supply chain configuration is and how many units should be produced in each period without extraneous manufacturing efforts, as well as the number of units to be moved from the manufacturer to the warehouse and from the warehouse to the consumer. Perishability of products, retailer demand, and inventory management will be based on the ages of products in the warehouse. As for perishable goods, the FIFO inventory policy is commonly used by producers, when it is preferred in the realworld sector since it prevents product waste and expiration.
Figure 1 shows the SCN as it consists of three potential suppliers, three potential manufacturers, and one warehouse to serve three customers.
Figure 1
Figure 1 Supplier, Manufacturer, Warehouse, and customer network 
2. MATHEMATICAL MODEL FORMULATION
2.1. NOTATIONS
Sets
S Suppliers.
M Manufacturers.
W Warehouse.
C Customers.
A Ages of stored products.
T Planning periods.
Parameters
Shelflife.
The demand of customers.
Supplier capacity.
Manufacturer capacity.
Hour’s capacity of manufacturer.
Warehouse capacity.
Price of customers.
Fixed cost of contracting supplier.
Fixed cost of opening manufacturing.
Fixed cost of warehouse.
Transportation cost per unit per distance.
Big number.
Distance between manufacturer and warehouse.
Distance between supplier and manufacturer.
Distance between warehouse and customers.
Inventory retention cost.
Expired cost.
Batch size from supplier.
Batch size from manufacturer.
Batch size from warehouse.
Material cost per unit supplied by supplier.
Manufacturer capacity cost per hour of the facility that is not utilized.
Shortage cost.
Material cost per unit for manufacturer.
Variables
The number of batches transported from supplier to the manufacturer.
The number of batches transported from manufacturer to the warehouse.
The number of batches transported from warehouse to the customer.
Inventory of age at the end of period.
Expired inventory at the end of period.
Binary variable equals 1 if facility i is open and 0 otherwise.
Binary variable equals 1 if a transportation link is activated between (w) and (m).
Binary variable equals 1 if a transportation link is activated between (s) and (m).
Binary variable equals 1 if a (c) is contracted and 0 otherwise.
Total profit.
2.2. OBJECTIVES FUNCTIONS
The objectives of the model are to maximize the profit, OCSLs of the three customers Equation 1 and consequently minimizing the total cost.
Subtraction of the total cost Equation 3, Equation 10 from the total revenue Equation 2 will result in the total profit.
Total cost = fixed costs + material costs + nonutilized capacity costs + shortage costs + transportation costs + manufacturing costs + inventory holding costs.
Equation 4
Equation 5
Equation 6
Equation 7
Equation 8
Equation 9
2.3. CONSTRAINTS
The following section represented constraints of the proposed model.
Constraint Equation 11 ensures that the supplier’s capacity does not exceed the sum of the flow exiting from each supplier to manufacturer, at each period.
Constraint Equation 12 guarantees that the manufacturer's prespecified capacity doesn’t exceed the number of units transferred from manufacturer to supplier.
Constraint Equation 13 ensures that the sum of production hours for all products manufactured in the warehouse is delivered to its store, in each period that does not exceed manufacturing capacity hours.
Constraint Equation 14 guarantees that the preselected capacity from the manufacturer will be equal to the number of units transferred from manufacturer to supplier.
Constraint Equation 15 guarantees that the warehouse capacity in the first period does not exceed the number of units transferred from the manufacturer to the warehouse.
Constraint Equation 16 guarantees that the total quantity of products entering the warehouse will not be exceeded the warehouse's prespecified capacity, in each period and products remaining from the previous period.
The FIFO policy is the best for the inventory of perishable products which has a short shelf life by its nature, to prevent product expiration and minimize the costs arising from those expired products as the policy prioritizes maximizing of the use of inventory by the oldest products that will be deteriorated first.
Equation 18
Constraints Equation 17, Equation 19 the warehouse at the end of each period is calculated by remaining inventory. They guarantee that the FIFO inventory policy has been applied. FIFO inventory policy will be used first to fulfil demand. The distribution age of the units in stock is monitored then the inventory of the intermediate age, and finally the demand will be fulfilled by inventory of the lowest age or the inventory of the freshest units.
Constraint Equation 20 guarantees that no expired inventory will arrive at the shelflife. Moreover constraint Equation 21 calculates the expired inventory that only appears after reaching shelf life.
As a result of adopting the FIFO inventory policy, the environmental impact is minimized by preventing the expiration of the products. Producing a sufficient quantity from the manufacturer to the warehouse according to the retailers’ demands and withdrawing from the old demand (FIFO), will result in the prevention of product expiration, in case of storing some quantities for the next periods. Saving the environment by preventing the expiration of production is important, as many energies and resources can be saved in processes, i.e., material, production, transportation, etc.
3. COMPUTATIONAL RESULTS AND ANALYSIS
3.1. MODEL VERIFICATION
The model which comprises six planning periods, three potential manufacturers, warehouse, and three customers. All the inputs in the experiments have fixed variables as presented in Table 1. It’s assumed that retailer demand values in the six periods are 5000, 6000, 7000, 8000, 9000, and 10000 units, respectively.
Table 1
Table 1 Model parameters 

Parameter 
Value 
Parameter 
Value 

10000
($) 

100
($) 

3
(Period) 

10
($) 

15
($) 

10
($) 

10
($) 

30,
40, 50 (Km) 

0.002
($) 

40,
50, 30 (Km) 

4
($) 

50,
30, 40 (Km) 

3
($) 

200,
100, 400 (Km) 

1 

200,
250, 300 (Km) 

1 

6000
(unit) 

1 

6000
(unit) 

10000 

6000
(hour) 

20000 

600000
(unit) 
3.2. RESULTS AND ANALYSIS
The number of units transferred from suppliers to manufacturers, the number of units transferred from the manufacturer to the warehouse, warehouse to the customer, and the inventory and expired quantities are presented in Table 2 and Table 3, Table 4 shows that the FIFO strategy has been used successfully to avoid aging of stored products and avoid expiration at a 0% deviation.
Table 2
Table 2 Number of units transferred from suppliers to manufacturers 

Supplier 1 
Supplier 2 
Supplier 3 

Period 
S_{1}M_{1} 
S_{1}M_{2} 
S_{1}M_{3} 
S_{2}M_{1} 
S_{2}M_{2} 
S_{2}M_{3} 
S_{3}M_{1} 
S_{3}M_{2} 
S_{3}M_{3} 
1 
6000 
0 
0 
0 
6000 
0 
0 
0 
6000 
2 
6000 
0 
0 
0 
6000 
0 
0 
0 
6000 
3 
6000 
0 
0 
0 
6000 
0 
0 
0 
6000 
4 
6000 
0 
0 
0 
6000 
0 
0 
0 
6000 
5 
6000 
0 
0 
0 
6000 
0 
0 
0 
6000 
6 
6000 
0 
0 
0 
6000 
0 
0 
0 
6000 
T 
36000 
0 
0 
0 
36000 
0 
0 
0 
36000 
108000 
Table 3
Table 3 Number of units transferred from the manufacturers to the warehouse, and from warehouse to the customers 

Manufacturers to the warehouse 
Warehouse to the customers 

Period 
M_{1}W 
M_{2}W 
M_{3}W 
WC_{1} 
WC_{2} 
WC_{3} 
1 
6000 
6000 
6000 
5000 
5000 
5000 
2 
6000 
6000 
6000 
6000 
6000 
6000 
3 
6000 
6000 
6000 
7000 
7000 
7000 
4 
6000 
6000 
6000 
8000 
8000 
2000 
5 
6000 
6000 
6000 
9000 
9000 
0 
6 
6000 
6000 
6000 
10000 
8000 
0 
T 
36000 
36000 
36000 
45000 
43000 
20000 
108000 
108000 
Table 4
Table 4 The inventory and expired quantities 

Period 
I_{at} 
I_{expt} 

a_{1} 
a_{2} 
a_{3} 

1 
3000 
0 
0 
0 
2 
3000 
0 
0 
0 
3 
0 
0 
0 
0 
4 
0 
0 
0 
0 
5 
0 
0 
0 
0 
6 
0 
0 
0 
0 
T 
6000 
0 
0 
0 
Figure 2 represents the production flow through the SCN in which the model optimization capability has been verified. It shows that customers’ demands in the first period have been fully met as it is less than the production capacity of the supply chain and an excess amount is stored to meet the increase in demand during the following periods when the volume of demand exceeds the production capacity. Figure 2 also shows the fulfilment of customer demands in the third period, although it exceeds the production capacity due to the quantity that was stored in the first period. While the requests for the fourth period and beyond were not met due to the lack of sufficient production capacity, which led to a gradual increase in the shortage.
Figure 2
Figure 2 Production flow. 
3.3. EFFECT OF THE MAXIMUM PERMISSIBLE DEVIATION ON SUPPLY CHAIN OBJECTIVES
While increasing the maximum permissible percent of deviation that decreases the profit values; the total cost will be increased as shown in Figure 3 and Figure 4. The total revenue remains constant at 10800000 $ in all cases. The OCSLs also does not changed and remain at 80% in all cases.
Figure 3
Figure 3 The resulted profit 
Figure 4
Figure 4 The resulted total cost 
3.4. EFFECT OF OPTIMIZATION ORDER ON SC OBJECTIVES
In this section, the effect of changing solution priorities on target values at 0% and 30% diffraction values will be studied. Table 5 shows the different arrangements for the objectives, which are 6 arrangements.
In this section, it was noticed that changing of objectives aimed at optimization of profit with lees total cost, and better OCSLs, using deviation 0%, and 30%. At 0% deviation and changing of objectives; ended up by PCS, PSC, SPC and SCP as the best result. In deviation 0.3; ended up by PCS and SCP as the best result.
Table 5
Table 5 Objectives orders 

Case 
1 
2 
3 
4 
5 
6 
Order 
PCS 
PSC 
SPC 
SCP 
CPS 
CSP 
P
= profit, S = OCSLs,
C = total cost 
It appears from the results shown in Figure 5 and Figure 6 when the allowable deviation percentage is 0% that the acceptable arrangements are the ones that start with maximizing profit or maximizing the OCSL, as the results showed that giving priority to reducing costs negatively affects the rationality of the results and thus the performance of the supply chain.
Figure 5
Figure 5 The resulted profit and total cost 
Figure 6
Figure 6 The resulted OCSLs 
Also, it appears from the results shown in Figure 7 and Figure 8 when the allowable deviation percentage is 30% that the accepEq arrangements are the ones that start only with maximizing profit. or, as the results showed that giving priority to maximizing the OCSL or reducing costs negatively affects the rationality of the results and thus the performance of the supply chain.
It is clear from this study that it is very important to arrange the targets and to choose the maximum allowable deviation. Therefore, researchers recommend the necessity of experimenting with many values and arrangements and comparing them according to the priorities of decisionmakers to choose the optimal design and planning for the supply chain as they see fit.
Figure 7
Figure 7 The resulted profit and total cost 
Figure 8
Figure 8 The resulted OCSLs 
4. CONCLUSION AND RECOMMENDATIONS
In this paper, a multiobjective sustainable supply chain network locationallocation model for perishable products has been developed to prevent the expiration of products considering the FIFO inventory policy to maximize the total profit of the network.
This model has successfully handled the problem of a multiobjective sustainable supply chain network location allocation for perishable products. It also helped in the prevention of product expiration by assuring that only the necessary quantities are produced without waste.
It is clear from this study that it is very important to arrange the targets and to choose the maximum allowable deviation. Therefore, researchers recommend the necessity of experimenting with many values and arrangements and comparing them according to the priorities of decisionmakers to choose the optimal design and planning for the supply chain as they see fit. The ordering of objectives influences the factory's success as well as their allowable deviation.
It is recommended to develop the model to tackle the uncertainty in both demand and production capacity to produce more practical solutions.
CONFLICT OF INTERESTS
None.
ACKNOWLEDGMENTS
None.
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